GENERAL MATHEMATICS-WASSCE/NOVDEC
Question 1
A = {2, 4, 6, 8}, B = {2, 3, 7, 9} and C = {x: 3 < x < 9} are subsets of the universal-set
U = {2, 3, 4, 5, 6, 7, 8, 9}. Find
(a) A n(B'nC');
(b) (AuB) n (BuC).
Question 2
(a) The angle of depression of a boat from the mid-point of a vertical cliff is 35°. If the boat is 120 m from the foot of the cliff, calculate the height of the cliff.
(b) Towns P and Q are x km apart. Two motorists set out at the same time from P to Q at steady speeds of 60 km/h and 80 km/h. The faster motorist got to Q 30 minutes earlier than the other. Find the value of x.
Question 3
(a) In the diagram, L PQR = 125°, LQRS = r, LRST = 800 and LSTU = 44°. Calculate the value of r
b) .
In the diagram, TS is a tangent to the circle at A. ABI ICE, LAEC = sx", LADB = 60° and LTAE = xo. Find the value of x",
Question 4
The diagram shows a cone with slant height 10.5 cm. If the curved surface area of the cone is 115.5 cm²;, calculate, correct to 3 significant figures, the:
(a)base radius, r;
(b)height, h;
(c)volume of the cone. [Taken= 22/7]
Question 5
Two fair dice are thrown.
M is the event described by "the sum of the scores is 10" and
N is the event described by "the difference between the scores is 3".
(a) Write out the elements of M and N.
(b) Find the probability of M or N.
(c) Are M and N mutually exclusive? Give reasons.
Question 6
(a)The scale of a map is 1:20,000. Calculate the area, in square centimetres, on the map of a forest reserve which covers 85 km²,
(b) A rectangular playing field is 18 m wide. It is surrounded by a path 6m wide such that its area is equal to the area of the path.
(C)Calculate the length of the field.
Question 8
Using ruler and a pair of compasses only,
(a) construct
(i) a quadrilateral PQRS with IPSI :: 6 cm, LRSP:: 90°,
IRSI = 9 ern, IQRI = 8.4 cm and IPQI :: 5.4 cm;
(ii) the bisectors of LRSP and LSPQ to meet at X;
(iii) The perpendicular XTto meet PS at T.
(b) Measure IXT/'
Question 9
In the diagram, /AB/ = 8 km, /BC/ = 13 km, the bearing of A from B is 310° and the bearing of B from C is 230°. Calculate, correct to 3 significant figures,
(a) the distance AC;
(b) the bearing of C from A;
(c) how far east of B, C is
Question 10
(a) Copy and complete the table of values for the relation V = -X² + X + 2 for -3 ≤ x ≥ 3.
(b) Using scales of 2 cm to 1 unit on the x-axis and 2 cm to 2 units on the v-axis, draw a graph of the relation
y = -X² + X + 2.
(c) From the graph, find the:
(i)Minimum value of y;
(ii)Roots of the equation X² - x -2 = 0;
(iii)Gradient of the curve at x = -0.5.
Question 11
In the diagram, L.PTQ = L.PSR = 900, /PQ/ = 10 ern, /PS/ = 14.4 cm and /TQ/ = 6 cm.
Calculate the area of quadrilateral QRST.
(b) Two opposite sides of a square are each decreased by 10% while the other two are each increased by 15% to form a rectangle. Find the ratio of the area of the rectangle to that of the square.
Question 12
The frequency distribution of the weight of 100 participants in a high jump competition is as
shown below:
Weight (kg)
20-29
30 - 39
40 - 49
SO - 59
60 - 69
70-79
Number ofparticipants
10
18
22
25
16
9
(a) Construct the cumulative frequency table.
Question 13
(a)The third term of a Geometric Progression (G.P) is 24 and its seventh term is 4(20/27) .Find Its irst term.
(b)Given that y varies directly as x and inversely as the square of z. If y = 4, when x = 3 and z = 1, find y when x = 3 and z = 2.
(b) Draw the cumulative frequency curve.
(c) From the curve, estimate the:
(i) median;
(ii) semi-interquartile range;
(iii) probability that a participant chosen at random weighs at least 60 kg.